Theorems · Theorem · commutative algebra
Ideal.finite_factors
∀ {R : Type u_1} [inst : CommRing R] [IsDedekindDomain R] {I : Ideal R}, I ≠ 0 → {v | v.asIdeal ∣ I}.FiniteOnly finitely many maximal ideals of R divide a given nonzero ideal.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDedekindDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypeproof · cited by 7,736
- Set.ofPredstatement · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Finiteproof · cited by 3,029
- Set.Finitestatement · cited by 1,814
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- Subtype.coe_injectiveproof · cited by 205
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement and proof · cited by 156
- Finite.of_injectiveproof · cited by 32
- Set.finite_coe_iffproof · cited by 21
Cited by7
Results whose statement or proof uses this declaration.
- NumberField.FinitePlace.hasFiniteMulSupport_intproof · cited by 3
- IsDedekindDomain.exists_sup_span_eqproof · cited by 2
- Ideal.map_algebraMap_eq_finsetProd_powproof · cited by 2
- Associates.finite_factorsproof · cited by 1
- FractionalIdeal.finite_factors'proof · cited by 1
- NumberField.FinitePlace.prod_eq_inv_abs_norm_intproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.Support.finiteproof · cited by 0